Inner uniqueness theorem for second order linear elliptic equation with constant coefficients

© 2015, Allerton Press, Inc. We consider solution f to a linear elliptic differential equation of second order, and prove that it vanishes if zeros of f condense to two points along non-collinear rays. The requirement of non-collinearity of the rays is essential if the roots of the characteristic equation are distinct. In the case of equal roots of the characteristic equation this property is valid if and only if the rays do not belong to common straight line